The polls, conducted by Democratic firms Global Strategy Group and Garin-Hart-Yang Research Group, found that more likely voters have an unfavorable view of Romney than a favorable one in five swing states: Colorado, Florida, Ohio, Pennsylvania, and Virginia.

Romney has an average favorable rating of only 36 percent in those states, with an average 43 percent unfavorable rating. Among independent voters, the ratio is worse: 30 percent favorable and 42 percent unfavorable. Thirty-seven percent of those polled said that Romney’s business record at Bain made them less likely to vote for him. Only 27 percent said it made them more likely to do so.

Romney has used his record at Bain, an investment firm, as evidence that he knows how to create jobs. Many of the ads run by Priorities USA in battleground states feature laid-off workers from plants that shut down under Bain’s management. A strategy memo circulated by Priorities USA cofounder Bill Burton in June said the attacks are resonating with “the actual voters who decide this election,” even if some pundits and other "elites" questioned the strategy.

To further test that theory, the pollsters compared perceptions of Romney across a set of comparable media markets, some where the ads were shown and others where they were not. Obama led Romney by 8 points in so-called “Priorities markets,” versus just 3 points in non-Priorities markets.

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Romney’s unfavorable rating was 9 points higher than his favorable rating in Priorities markets; the gap was only 5 points where the ads were not shown. Among voters who had seen the Bain attacks, Obama had an 11-point advantage on the question of whether the candidate “is honest and someone you can trust.”

Independent polling conducted by news organizations has split over whether the attacks have been effective at the national level. An NBC/Wall Street Journalpoll conducted in late June showed that 23 percent of the 1,000 adults surveyed viewed Romney in a more positive light because of his business record, while 28 percent said it made them view him more negatively. This trend was accentuated in swing states, the poll’s findings showed, where only 18 percent had a positive view of Romney’s business experience compared with 33 percent with a negative view.

But another national poll, an ABC News/Washington Postpoll of approximately the same number of adults this month, found that respondents were evenly divided over whether Romney’s time at Bain is a reason to support him (23 percent) or oppose him (24 percent). Fifty percent of people surveyed said it didn’t make a difference.

Romney’s campaign may be feeling some heat. The candidate finally began to turn Obama's attacks on his private-sector record against him Tuesday when he labeled Obama the true “outsourcer in chief” for investing U.S. money in energy companies that make products abroad.

The Priorities USA polls were based on interviews with more than 3,800 likely voters across five states, conducted June 25-July 3. The margin of error is plus or minus 2 percentage points.